Enter on L, find work as foreign expert, change to Z

I am 62, and schools in China won't hire me because, even though I am a healthy, fit, highly experienced, expert foreign ESL teacher who is a native speaker from Australia, I am over 60. (It is apparently better to hire inexperienced young people who are there mainly for a good time!) I am wondering if I could go on an L, find a private employer who doesn't advertise on job agency sites, who wants an expert to teach his own kids or something, and will provide the necessary documentation for me to get the z, can I change my L to a z, either in mainland or in Hongkong?